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# Four Questions on Probability

A) P(x > 74) in a normally distributed set of data with a mean of 62 and a standard deviation of 9.

b) P(49 < x < 78) in a normally distributed set of data with a mean of 62 and a standard deviation of 9.

c) The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. If 40 snowfall amounts are randomly selected, find u x-bar for the sampling distribution of sample means with samples of size 40.

d) For drivers in the 20-24 age bracket, there is a 34% rate of car accidents in one year (based on data from the National Safety Council.) An insurance investigator finds that in a group of 500 randomly selected drivers aged 20-24 living in New York City, 40% had accidents in the last year. If the 34% rate is correct, estimate the probability that in a group of 500 randomly selected drivers, at least 40% had accidents in the last year. Based on that result, is there strong evidence supporting the claim that the accident rate in New York City is higher than 34%?

#### Solution Summary

Detailed solutions to all the four questions are provided.

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